CN113219989B - Mobile robot path planning method based on improved butterfly optimization algorithm - Google Patents

Mobile robot path planning method based on improved butterfly optimization algorithm Download PDF

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CN113219989B
CN113219989B CN202110613592.4A CN202110613592A CN113219989B CN 113219989 B CN113219989 B CN 113219989B CN 202110613592 A CN202110613592 A CN 202110613592A CN 113219989 B CN113219989 B CN 113219989B
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butterfly
path
iteration
mobile robot
algorithm
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马小陆
梅宏
谭毅波
王兵
唐得志
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Jiangsu Province Nanjing University Of Science And Technology Electronic Information Technology Co ltd
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Anhui University of Technology AHUT
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0221—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving a learning process

Abstract

The invention discloses a mobile robot path planning method based on an improved butterfly optimization algorithm, which comprises the following steps: modeling a working space of the mobile robot by using a grid method; setting initial parameters of a butterfly optimization algorithm; setting a starting position and a target position of an algorithm; searching an optimal path, initializing a tabu table and adding the tabu table into the initial position of the butterfly; calculating the fragrance intensity generated by the current position of each butterfly, searching a subsequent transfer node by using the transfer probability, and stopping searching until the butterfly reaches a target position; judging whether the iteration times of the algorithm reach the maximum value, if so, keeping the shortest path, otherwise, continuing path optimization until the optimal path is searched; smoothing the searched path and outputting a smooth path; through simulation experiments, the method provided by the invention is verified to solve the problem of path planning of the mobile robot, and is an effective and feasible optimization algorithm.

Description

Mobile robot path planning method based on improved butterfly optimization algorithm
Technical Field
The invention relates to the field of mobile robot path planning, in particular to a mobile robot path planning method based on a butterfly optimization algorithm.
Background
In recent years, path planning is becoming more and more important in the field of robotics, and mainly aims to plan a collision-free path from a starting point to a target point under a known or unknown environment. Currently, path planning is mainly studied in depth from two aspects of global path planning and local path planning. The research of global path planning is to realize that the distance from the initial position to the target position of the robot is shortest, the time is the least and the energy consumption is the lowest on the basis of no collision. Common global path planning algorithms include an a-star algorithm, a Dijkstra algorithm, a particle swarm algorithm, an ant colony algorithm, and the like. The research of the local path planning aims to realize that the path turning points of the robot are fewer, the solution quality is better and the path is smoother. Common local path planning algorithms include a fuzzy logic algorithm, a rolling window algorithm, an artificial potential field algorithm and the like.
The butterfly optimization algorithm is a novel natural heuristic algorithm proposed by scholars such as Sankala pArora and the like in 2018 according to characteristics of foraging and idoring seeking behaviors of butterflies, and has the advantages of simplicity, easiness in implementation, high global search efficiency and the like. However, the butterfly optimization algorithm still has some problems in the path optimization process: generating an invalid path to influence the optimizing efficiency; no subsequent expansion node exists in the optimizing process, so that the robot is in a 'false death' state; the path at the turning point is not smooth enough, which is not beneficial to the walking of the mobile robot.
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a mobile robot path planning method based on a butterfly optimization algorithm, which can effectively solve the problem that an invalid path is generated by the algorithm and improve the global planning efficiency; solving the problem of no subsequent expansion node, and avoiding falling into local optimal solution; the problem of mechanical turning of the robot is solved, and a smooth path is planned.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that:
a mobile robot path planning method based on an improved butterfly optimization algorithm comprises the following steps:
step 1, rasterizing a working space of a mobile robot by using a grid method;
initializing relevant parameters of a butterfly optimization algorithm, including a butterfly population number M, a maximum iteration number T, a conversion probability P, a butterfly sensory form c and a power exponent a;
step 3, determining an initial position S and a target position G of the mobile robot in the grid map, placing M butterflies in the initial position S, and storing the current positions in a Tabu table Tabu;
step 4, calculating the fragrance intensity generated by the current position of each butterfly;
step 5, calculating the aroma concentration of 8 adjacent nodes of each butterfly at the current position, switching the global search and the local search by converting the probability P, and calculating the subsequent mobile node of the ith butterfly at the time t;
step 6, storing the current node after the ith butterfly reaches the subsequent nodeTabu in Tabu listiPerforming the following steps;
step 7, judging whether the butterfly reaches the target position G, if so, ending the current iteration, and ending the iteration; otherwise, repeating the steps 4-7 until the target position is searched;
step 8, after one iteration is finished and all butterflies reach the target positions G, evaluating and ranking the searched paths of all butterflies, and emptying Tabu tables;
step 9, judging whether the current iteration time T reaches the maximum iteration time T, if so, ending the path search, and turning to step 10; otherwise, repeating the steps 3-9, and continuing iterative search;
step 10: and taking the key nodes in the optimal path obtained by the algorithm as control points, constructing the control points by a cubic B-spline function, fitting the whole path according to the construction function to obtain a smooth path, and finally outputting the optimal path.
Preferably, the grids in the grid map are numbered, the coordinates (x) of the ith gridi,yi) The following were used:
Figure BDA0003097056130000021
wherein mod is a remainder operator; ceil is a backward integer; l is the side length of the grid; partitioning a workspace into N in units of LxRow and NyAnd (4) columns.
Preferably, the butterfly individual generates a flavour intensity f during foragingiThe calculation is as follows:
fi＝cIα
Figure BDA0003097056130000031
wherein f isiThe intensity of the ambient aroma perceived by the ith butterfly; i is the stimulation intensity; alpha is a power exponent; c is the sensory mode of the butterfly individual, and the value of c changes along with the change of the iteration number tInstead, the update strategy is shown in the following equation:
ct+1＝ct+(0.025(ct×Mmax))
preferably, in the foraging process, in order to improve the global search capability, the global search and the local search are switched by the conversion probability P in the moving process of the butterfly, and [0,1 ] is randomly generated in each iteration process]A random number r in1In comparison with the transition probability P, the butterfly state transition formula is as follows:
Figure BDA0003097056130000032
wherein the content of the first and second substances,
Figure BDA0003097056130000033
and
Figure BDA0003097056130000034
the spatial positions of the ith butterfly in the t iteration and the t +1 iteration respectively;
Figure BDA0003097056130000035
the spatial position of the jth butterfly in the t iteration is shown; r is [0,1 ]]A random number within; gbestThe spatial position of the optimal butterfly in the current iteration.
Preferably, the key nodes in the optimal path obtained by the algorithm are used as control points, the control points are subjected to cubic B-spline function construction, and then the whole path is subjected to fitting processing according to the construction function, so as to obtain a smooth path, wherein the path smoothing formula is calculated as follows:
Figure BDA0003097056130000036
Figure BDA0003097056130000037
wherein, PiCoordinates for a given n +1 control points; fi,3(t) is a 3-degree B-spline basis function.
The invention has the beneficial effects that:
the invention provides an improved path planning method aiming at the problems of low search efficiency, unsmooth path and the like of the current mainstream mobile robot path planning method. According to the method, a grid map is adopted to model the environment, and a tabu table and a backtracking method are adopted to avoid the condition that no subsequent expansion node exists when the path is optimized, so that the global search capability of the algorithm is improved, the path is smoothly processed by means of a cubic B-spline curve, the quality of the final path is greatly improved, and the effectiveness and the feasibility of the improved butterfly optimization algorithm for solving the path planning of the mobile robot are verified through an MATLAB simulation experiment.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the description below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of a path planning algorithm of the present invention;
FIG. 2 is a simulation result of path planning of three algorithms under a complex environment;
FIG. 3 is a line graph of the optimal path length which is planned by three algorithms under a complex environment and changes along with the increase of the iteration times.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-3, the present invention provides a technical solution: a mobile robot path planning method based on an improved butterfly optimization algorithm comprises the following steps:
step 1: rasterizing a working space of the mobile robot, and dividing a map into a plurality of bounded units without obstacles by using a map division algorithm, wherein the specific formula is as follows:
Figure BDA0003097056130000051
wherein (x)i,yi) Coordinates of the ith grid; l is the side length of the grid; partitioning a workspace into N in units of LxRow and NyColumns;
and 2, step: initializing parameters of a butterfly optimization algorithm, including a butterfly population number M, a maximum iteration number T, a conversion probability P, a butterfly sensory form c and a power exponent a;
and step 3: determining an initial position S and a target position G of the mobile robot in a grid map, placing M butterflies at the initial position S, and storing the current positions in a Tabu table Tabu;
and 4, step 4: calculating the fragrance intensity f generated by the current position of each butterflyiThe concrete formula is as follows:
fi＝cIα
Figure BDA0003097056130000052
wherein, fiThe intensity of the ambient aroma perceived by the ith butterfly; i is the stimulation intensity; alpha is a power exponent; c is the sensory mode of the butterfly individual, the value of which changes along with the change of the iteration times t, and the specific formula is as follows:
ct+1＝ct+(0.025(ct×Mmax))
and 5: the aroma concentration of 8 adjacent nodes of each butterfly is calculated at the current position, the probability P is converted to switch between global search and local search, and the subsequent mobile node of the ith butterfly at the moment t is calculated, wherein the specific formula is as follows:
Figure BDA0003097056130000053
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003097056130000054
and
Figure BDA0003097056130000055
the spatial positions of the ith butterfly in the t iteration and the t +1 iteration respectively;
Figure BDA0003097056130000061
the spatial position of the jth butterfly in the t iteration is shown; r is [0,1 ]]A random number within; gbestThe space position of the optimal butterfly in the current iteration is determined;
step 6: after the ith butterfly reaches the subsequent node, the current node is stored in a Tabu tableiPerforming the following steps;
and 7: judging whether the butterfly reaches a target position G, if so, ending the current iteration, and ending the iteration; otherwise, repeating the steps 4-7 until the target position is searched;
and step 8: after one iteration is finished and all butterflies reach the target position G, evaluating and ranking the searched paths of all the butterflies, and emptying Tabu tables;
and step 9: judging whether the current iteration time T reaches the maximum iteration time T, if so, ending the path search, and turning to the step 10; otherwise, repeating the steps 3-9, and continuing iterative search;
step 10: taking a key node in the optimal path obtained by the algorithm as a control point, constructing the control point by a cubic B-spline function, fitting the whole path according to the construction function to obtain a smooth path, and finally outputting the optimal path, wherein the specific formula is as follows:
Figure BDA0003097056130000062
Figure BDA0003097056130000063
wherein, PiCoordinates for a given n +1 control points; fi,3(t) is a 3-degree B-spline basis function.
Example (b):
in order to verify the effectiveness and feasibility of the invention, a grid method is used to establish a 20 × 20 grid working environment, the path searched by the improved butterfly optimization algorithm of the invention, the ant colony algorithm and the genetic algorithm are respectively subjected to simulation experiments under the same conditions, and the experimental results are shown in fig. 2 and fig. 3.
According to the comparison and analysis of the simulation experiment, the path planning problem of the mobile robot can be effectively solved, and compared with the path generated by the ant colony algorithm and the genetic algorithm, the path planning method has the advantages of higher path optimizing speed, better stability, higher efficiency and better solution quality, and is an effective and feasible path planning algorithm.
In the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims (3)

1. A mobile robot path planning method based on an improved butterfly optimization algorithm is characterized by comprising the following steps:
step 1, rasterizing a working space of a mobile robot by using a grid method;
initializing relevant parameters of a butterfly optimization algorithm, including a butterfly population number M, a maximum iteration number T, a conversion probability P, a butterfly sensory form c and a power exponent a;
step 3, determining an initial position S and a target position G of the mobile robot in the grid map, placing M butterflies in the initial position S, and storing the current positions in a Tabu table Tabu;
step 4, calculating the fragrance intensity generated by the current position of each butterfly;
step 5, calculating the aroma concentration of 8 adjacent nodes of each butterfly at the current position, switching the global search and the local search by converting the probability P, and calculating the subsequent mobile node of the ith butterfly at the time t;
step 6, after the ith butterfly reaches the subsequent node, storing the current node in a Tabu table TabuiPerforming the following steps;
step 7, judging whether the butterfly reaches the target position G, if so, ending the current iteration, and ending the iteration; otherwise, repeating the steps 4-7 until the target position is searched;
step 8, after one iteration is finished and all butterflies reach the target position G, evaluating and ranking the searched paths of all the butterflies, and emptying Tabu tables;
step 9, judging whether the current iteration time T reaches the maximum iteration time T, if so, ending the path search, and turning to step 10; otherwise, repeating the steps 3-9, and continuing iterative search;
step 10: taking key nodes in the optimal path obtained by the algorithm as control points, constructing the control points by a cubic B-spline function, fitting the whole path according to the construction function to obtain a smooth path, and outputting the optimal path;
the aroma intensity produced by butterfly individuals during foraging was calculated as follows:
Figure 100001_IMG2
Figure 100001_IMG3
wherein the content of the first and second substances,
Figure 100001_IMG4
the intensity of the ambient aroma perceived by the ith butterfly; i is the stimulation intensity; alpha is a power exponent; c is the sensory mode of the butterfly individual, the value of the sensory mode changes along with the change of the iteration times t, and the updating strategy is shown in the following formula:
Figure 100001_IMG5
in the foraging process, in order to improve the global search capability, the butterfly switches the global search and the local search by the conversion probability P in the moving process, and [0,1 ] is randomly generated in each iteration process]A random number r in1In comparison with the transition probability P, the butterfly state transition formula is as follows:
Figure 100001_IMG6
wherein the content of the first and second substances,
Figure 100001_IMG7
and
Figure 100001_IMG8
is the ith butterflySpatial positions in the t-th iteration and the t + 1-th iteration, respectively;
Figure 100001_IMG9
the spatial position of the jth butterfly in the t iteration is shown; r is [0,1 ]]A random number within; gbestThe spatial position of the optimal butterfly in the current iteration.
2. The method for mobile robot path planning based on improved butterfly optimization algorithm according to claim 1, further comprising:
numbering grids in a grid map, the coordinates of the ith grid
Figure 100001_IMG10
The following were used:
Figure 100001_IMG11
wherein mod is a remainder operator; ceil is a backward integer; l is the side length of the grid; partitioning a workspace into N in units of LxRow and NyAnd (4) columns.
3. The method for mobile robot path planning based on improved butterfly optimization algorithm according to claim 1, further comprising:
taking a key node in the optimal path obtained by the algorithm as a control point, constructing a cubic B-spline function on the control point, and fitting the whole path according to the construction function to obtain a smooth path, wherein the path smoothing formula is calculated as follows:
Figure 100001_IMG12
Figure 100001_IMG13
wherein, PiCoordinates for a given n +1 control points;
Figure 100001_IMG14
is a 3-degree B-spline basis function.
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